How do I predict the occurrence of rare events?
It might be more informative to:


Label each combination of location, type, and time of crime with a crime rate. For example, theft, in Crystal City, at 11pm at night, occurs 20 times per year, or 0.4 times per resident per year.
Predict the crime rate, rather than individual events.


This avoids the need to have explicit examples of "non-crime", and lets you instead directly learn something related to the probabilities of crimes being committed (the rate).